Compound interest

In the second fundamental regime the interest that accrues does not stay still: it is added to the capital and in turn begins to produce interest. This is the mechanism that makes growth exponential.

Definition — Compound interest

In the same scenario with compound capitalisation, interest is added to the capital at the end of each period and in turn generates interest: $M = C_0\,(1+i)^t.$ The amount grows exponentially.

The factor $(1+i)$ acts at each period on the whole accumulated amount, not on the initial capital alone: hence the $t$-th power and the exponential growth, which over the long run clearly outstrips the linear growth of simple interest.

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Topics: Percentages
Concepts: Compound capitalisation · Exponential growth · Interest · Compound interest
Methods: Compound interest
Skills: Using formulae